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Doctoral Thesis
DOI
https://doi.org/10.11606/T.8.2013.tde-18042013-120246
Document
Author
Full name
Luciano Vicente
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2013
Supervisor
Committee
Loparic, Andrea Maria Altino de Campos (President)
Coelho, Antonio Mariano Nogueira
Guerzoni, José Alexandre Durry
Pereira, Luiz Carlos Pinheiro Dias
Santos, Luiz Henrique Lopes dos
Title in Portuguese
Definições parciais de verdade e sistemas de acumulação na aritmética formal
Keywords in Portuguese
Definições parciais de verdade
Sistemas de acumulação
Abstract in Portuguese
Segundo o teorema da indefinibilidade de Tarski-Gödel, não existe fórmula da linguagem da aritmética que defina o conjunto dos números de Gödel das sentenças verdadeiras da aritmética. No entanto, para cada número natural n, podemos definir o conjunto dos números de Gödel das sentenças verdadeiras da aritmética de grau menor que n. Essas definições produzem uma hierarquia V0(x), V1(x),..., Vn(x),... tal que, para todo x, se Vn(x), então Vn+1(x). Nesse estudo, ensairemos algumas aplicações desses predicados, chamados definições parciais de verdade, e outros predicados relacionados a eles na construção de sistemas formais para as verdades da aritmética. A ideia subjacente aos nossos sistemas é muito simples, devemos acumular de alguma maneira as definições parciais de verdade. Grosso modo, mostrar como fazê-lo é o objetivo desse estudo.
Title in English
Partial truth definitions and accumulation systems in formal arithmetic
Keywords in English
Accumulation systems
Partial truth definitions
Abstract in English
According to Tarski-Gödels undefinability theorem, there is no formula in the language of arithmetic which defines the set of Gödel numbers of arithmetical true sentences. Nevertheless, for each n, we can define the set of Gödel numbers of all arithmetical true sentences of degree n or less. These definitions yield a hierarchy of predicates V0(x), V1(x),..., Vn(x),... such that, for all x, if Vn(x), then Vn+1(x). In this study, we will ensay some aplications of these predicates, called partial truth definitions, and others related ones in building of formal systems for arithmetical truth. The underlying idea of our systems is very simple, we should accumulate in some way the partial truth definitions. Roughly speaking, showing how we can do that is the aim of this study.
 
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Publishing Date
2013-04-18
 
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